Basic principles of growing the thick (35-60 m) single-crystalline La-substituted yttriumiron garnet (Y3− La Fe5O12, La : YIG) films with reproducible parameters have been formulated. La : YIG films are grown on gallium-gadolinium garnet (Gd3Ga5O12) substrates from a supercooled melt-solution (MS) consisting of Y2O3, La2O3, and Fe2O3 oxides and the PbO-B2O3 solvent. In order to minimize the implantation of Pb 2 + ions into the films, which degrades the film quality, the epitaxy has to be performed at high temperatures and a low MS supercooling. It is found that, in order to maintain a constant growth rate of La : YIG films with reproducible parameters, a large MS mass (10-16 kg) has to be used, and the MS temperature has to be permanently lowered at a rate of 0.042 K/min.